The present invention relates to a method for controlling an electric motor and an apparatus for controlling the same, which method suppress vibrations of the electric motor or control object, resulting from a shortage in mechanical rigidity of a control object itself of the motor and a coupling shaft for connecting the motor and control object.
In positioning control which uses an electric motor, a digital servo control using a microcomputer has been conventionally employed. An apparatus for controlling an electric motor according to a prior art example, which has an object to suppress and prevent vibrations, has been disclosed in the Institute of Electrical Engineers National Convention No. 1759 “Vibration Suppression Control of Torsional Vibrations in Reduction Gears” in 1993.
A description is given of an apparatus for controlling an electric motor according to the prior art example. FIG. 26 is a configurational view of an apparatus for controlling an electric motor according to the prior art example. In FIG. 26, reference number 101 denotes a position instruction implementing section, 102 denotes an electric motor, 103 denotes a control object to be controlled, 104 denotes a position detecting section, and 105 denotes a servo controller. The servo controller 105 includes a position instruction inputting section 106, a prefilter section 107, and an instruction follow-up controlling section 108. The instruction follow-up controlling section 108 includes a position deviation calculating section (subtractor) 109, a position controlling section 110, a speed calculating section 111, a speed deviation calculating section (subtractor) 112, a speed controlling section 113, and a current controlling section 114. Reference symbol s denotes a Laplacian (Laplace operator).
The position instruction implementing section 101 prepares a position instruction and inputs it into the position instruction inputting portion 106 of the servo controller 105. The position instruction inputting portion 106 transmits a position instruction θM* to the instruction follow-up controlling section 108 via the prefilter section 107. The controlling apparatus according to the prior art example controls an electric motor 102 so that the position (hereinafter called “Control object position θL”) of a control object (load) 103 to be controlled, which is coupled to the electric motor is made coincident with the position instruction θ*. In FIG. 26, no control object position θL can be detected. The position detecting section 104 detects the position (hereinafter called “Electric motor position θM”) of the electric motor 102. The servo controller 105 controls the electric motor 102 so that the electric motor position θM is made coincident with the position instruction θ*, whereby the controlling apparatus according to the prior art example controls the electric motor 102 so that the control object position θL is made coincident with the position instruction θ*. The electric motor position θM and control object position θL are controlled so as to quickly follow up with the position instruction θ*.
In a control system in which the rigidity of a control object 103 itself and of a coupling shaft for connecting the electric motor 102 and the control object 103 is high, the controlling apparatus according to the prior art example is able to control the electric motor 102 so that the control object position θL becomes coincident with the position instruction θ* at high accuracy.
In a control system in which the rigidity of a control object 103 itself and of a coupling shaft for connecting the electric motor 102 and the control object 103 is low (including a control system capable of controlling at high accuracy to such a degree that the torsion, etc. of the coupling shaft cannot be ignored), a phase arises between the control object position θL and the electric motor position θM, torsional vibration of the coupling shaft is liable to occur. In a controlling apparatus that controls the electric motor 102 so that the electric motor position θM is made coincident with the position instruction θ*, if vibration occurs due to torsion of the coupling shaft, the rate of the control object position θL converging on the position instruction θ* becomes slow.
In the prior art example, the prefilter section 107 inputs a pattern of the position instruction θ* and varies it to a pattern θM* (electric motor position instruction) which does not cause vibrations of the control object position θL. The instruction follow-up controlling section 108 controls the electric motor 102 so that the electric motor position θM is made coincident with the control object position θL. The prefilter section 107 suppresses vibration of the control object position θL and speeds up the rate of convergence of the electric motor position θM and control object position θL on the position instruction θ*.
A description is given of a flow of basic calculations in the prior art controlling apparatus shown in FIG. 26. The position instruction inputting section 106 inputs a position instruction prepared by the position instruction implementing section 101. The position instruction inputting section 106 converts the inputted position instruction in units, and produces and outputs a position instruction θ* in agreement with the unit system used in calculations in the servo controller 105.
The prefilter section 107 differentiates the position instruction θ* in the second order and calculates a vibration suppression compensating value obtained by multiplying the output by a prescribed coefficient 1/(ωa2). The prefilter section 107 adds the position instruction θ* and the calculated vibration suppression compensating value to each other, and generates and outputs an electric motor position instruction θM*. Where it is assumed that the anti-resonance frequency is fr, which is included in a system from the torque outputted by the electric motor to the electric motor 102, preferably ωa=2π·f (f is a frequency of fr or a frequency in the vicinity of fr) may be established. The principle for suppressing vibrations by the prefilter section 107 is described later.
A detailed description is given of a flow of internal calculations in the instruction follow-up controlling section 108. The position deviation calculating section (subtractor) 109 inputs the electric motor position instruction θM* and electric motor position θM, and calculates an electric motor position deviation ΔθM (=θM*−θM). The position controlling section 110 outputs a speed instruction ωM* (=Kpp·θM) by using position proportional gain Kpp.
The speed calculating section 111 differentiates the electric motor position θM and calculates the electric motor speed ωM(=ωM·s). The speed deviation calculating section (subtractor) 112 inputs a speed instruction ωM* and an electric motor speed ωM. And it calculates a speed deviation ΔωM (=ωM*−ωM).
The speed controlling section 113 carries out a proportional integral calculation on the basis of the speed deviation ΔωM, and outputs a torque instruction T*. The current controlling section 114 controls a current value I flowing into the electric motor 102 so that the torque TM outputted by the electric motor 102 becomes T*.
A description is given of the principle of suppressing vibrations by the prefilter section 107. A system in which the electric motor 102 drives the control object 103 is expressed by using a two-inertia system (electric motor 102 and control object 103) as a model (FIG. 27). The model is generally used as a model of a resonance system. Actually, a system in which the torque TM drives the control object position θL may be expressed by a complicated mathematical expression model.
FIG. 28 is a block diagram expressing a system, in which the electric motor 102 shown in FIG. 27 drives the control object 103 via a coupling shaft having low rigidity, in terms of a mathematical expression model. In FIG. 28, the electric motor 102 generates an actual torque TM at a sufficiently quick response in accordance with the torque instruction T*. It is assumed that a transmission function from input of the torque instruction T* to generation of an actual torque TM is TM/T*=1. Reference symbol JM denotes inertia of the electric motor 102, JL denotes inertia of the control object 103, and Ks denotes a spring constant of the coupling shaft. Inertia of the coupling shaft is ignored since it is considered that it is sufficiently small in comparison with JM and JL.
If the transmission function θM/T* from the torque instruction T* to the electric motor position θM is obtained on the basis of the mathematical expression model shown in FIG. 28, Expression (1) can be brought about.(JLs2+Ks)/[{JM·JLs2+Ks(JM+JL)}s2]  (1)
If the transmission function θL/θM from the electric motor position θM to the control object position θL is obtained on the basis of the mathematical expression model shown in FIG. 28, Expression (2) can be brought about.Ks/(JLs2+Ks)  (2)
FIG. 29 is a block diagram expressed by a Laplacian (Laplace operator) s equivalent to the configuration view of FIG. 26, using Expressions (1) and (2) obtained from the block diagram of FIG. 28. In FIG. 29, blocks having the same number as those of FIG. 26 have the same functions as those of FIG. 26.
In FIG. 29, where no prefilter section 107 is provided, the position instruction θ* is equal to θM* (that is, θ*=θM*). A description is given of a difference in response between the case where no prefilter section 107 is provided and the case where the prefilter section is provided, by comparing the transmission function from the electric motor position instruction θM* to the control object position θL with the transmission function from the position instruction θ* to the control object position θL in FIG. 29.
A description is given of the frequency characteristics where no prefilter section 107 is provided, that is, those of the transmission function from the electric motor position instruction θM* to the control object position θL in FIG. 29. The frequency characteristics of the transmission function from the torque instruction T* to the electric motor position θM in FIG. 29 become as in FIG. 30(a) on the basis of Expression (1). In FIG. 30(a), the abscissa indicates frequency while the ordinate indicates gain and phase. The abscissa is expressed in terms of a logarithm. In the other frequency characteristic diagrams, the abscissa indicates frequency while the ordinate indicates gain and phase. In addition, the abscissa is expressed in terms of a logarithm.
Since the rigidity of the control object is low, FIG. 30(a) has a resonance point and an anti-resonance point. In FIG. 30(a), frequency in which resonance is generated is called a resonance frequency, and frequency in which anti-resonance is generated is called an anti-resonance frequency. The frequency characteristics of a transmission function including a system of a feedback loop from the electric motor position instruction θM* to the electric motor position θM become as in FIG. 30(b).
The frequency characteristics of the transmission function from the electric motor position θM to the control object position θL become as in FIG. 30(c) on the basis of Expression (2). The frequency characteristics of the transmission function from the electric motor position instruction θM* to the control object position θL (the response frequency characteristics of the controlling apparatus where no prefilter section 107 is provided) become as in FIG. 30(d), by combining FIG. 30(b) and FIG. 30(c) together. FIG. 30(d) has the gain peak in the anti-resonance frequency fr.
FIG. 31(a) shows a pattern of the electric motor position instruction θM* instructing that the position of the electric motor 102 is changed by a fixed amount. The ordinate indicates the electric motor position instruction θM* (an amount of change in the position of the electric motor 102), and the abscissa indicates time. This is an S-letter instruction that is generally used. FIG. 31(b) shows a differential waveform of the electric motor position instruction θM* of FIG. 31(a) and becomes a trapezoidal pattern. FIG. 32 shows response of the electric motor position deviation ΔθM at this time and response of the control object position deviation ΔθL, which is a difference between the control object position θL and the electric motor position instruction θM*. The period of a position instruction output of FIG. 32 indicates a period during which the electric motor position instruction θM* of FIG. 31(a) is fluctuating, that is, a period during which the differential value of the electric motor position instruction θM* of FIG. 31(b) is not zero.
As shown in FIG. 32, after the position instruction output is completed, the control object position deviation ΔθL greatly vibrates in comparison with the electric motor position deviation ΔθM. If the vibration frequency of the control object position θL is measured, the vibration frequency becomes a frequency in the vicinity of the frequency (anti-resonance frequency) at which the gain peak is produced in the frequency characteristics of the transmission function from the electric motor position instruction θM* to the control object position θL, which is shown in FIG. 30(d). Resulting from low rigidity in the shaft coupling the electric motor 102 to the control object 103, the control object position θL greatly generates vibrations after the position instruction output is completed.
Next, a description is given of frequency characteristics where the prefilter section 107 is provided, that is, frequency characteristics of the transmission function from the position instruction θ* to the control object position θL of FIG. 29. The frequency characteristics of the transmission function from the electric motor position instruction θM* to the control object position θL become as in FIG. 30(d). The frequency characteristics of the prefilter section 107 become as in FIG. 33(a) where it is assumed that ωa=2π·fr is established (fr is an anti-resonance frequency in FIG. 30(a)). The prefilter section 107 has frequency characteristics in which the gain is minimized at the frequency ωa, and gain is increased in line with an increase in frequency at a higher range than ωa. The frequency characteristics of the transmission function from the position instruction θ* to the control object position θL become as in FIG. 33(b) by combining FIG. 30(d) and FIG. 33(a) together.
If FIG. 33(b) is compared with FIG. 30(d) showing the frequency characteristics of the transmission function from the position instruction to the control object position θL where no prefilter section 107 is provided, no gain peak is provided at the anti-resonance frequency in FIG. 33(b). That is, the prefilter section 107 lowers the gain peak at the anti-resonance frequency in the response characteristics of the controlling apparatus.
In the case where the instruction pattern of the position instruction θ* is as in FIG. 31(a), the response of the control object position deviation ΔθL and the electric motor position deviation ΔθM are shown in FIG. 34. If it is compared with FIG. 32 showing a response where no prefilter section 107 is provided, vibration of the control object position θL is decreased after the position instruction output is completed. The response of FIG. 32 is the same as that of FIG. 34 with respect to the construction other than the prefilter section 107 shown in FIG. 29.
As described above, in the prior art controlling apparatus, the prefilter section 107 shown in FIG. 26 lowers the gain peak produced in the frequency characteristics of the transmission frequency from the position instruction θ* to the control object position θL, whereby vibration of the control object position ΔL is decreased, which is generated after the position instruction output is completed, resulting from the gain peak.
FIG. 35 shows response characteristics in the case where the parameter settings of a system having the response characteristics shown in FIG. 32 are partially varied. In the system shown in FIG. 35, in comparison with the system shown in FIG. 32, position proportional gain Kpp of the position controlling section 110 and speed proportional gain Kvp of the speed controlling section 113 are lowered, and vibration is reduced after the position instruction output of the control object position θL is completed. In FIG. 35, the vibration amplitude upon completion of the position instruction output is almost equivalent to that of FIG. 34. However, the response thereof is made slower than that of FIG. 34.
In the controlling apparatus according to the prior art example, the prefilter section 107 can bring about an effect by which vibrations of the control object position θL can be lowered after a position instruction output is completed while maintaining high response performance of the controlling apparatus.
In the prior art example, where it is assumed that a position instruction θ* outputted by the position instruction inputting section 106 of FIG. 29 has a pattern shown in FIG. 31(a), the instruction pattern of the electric motor position instruction θM* passing through the prefilter section 107 (the transmission function has a correction term (s2/ωa2) of the second order differential of the position instruction) becomes as in FIG. 36. In FIG. 31(b) and FIG. 36, points A, B, C and D are points of acceleration fluctuation (second order differentials of the position instruction) of the instruction pattern of FIG. 31(a). The second order differential of the electric motor position instruction θM* radically fluctuates at the points A, B, C and D. FIG. 37 shows a waveform of the torque instruction T* where the system shown in FIG. 29 inputs a position instruction θ* of the instruction pattern of FIG. 31(a).
At the points A, B, C and D, a very large torque instruction T*, which is shown by a broken line circle of FIG. 37, is generated resulting from radical fluctuations of the second order differential of the electric motor position instruction θM*. At the points A, B, C and D, the greater the second order differential of the electric motor position instruction θM* is, that is, the smaller the ωa is, or the greater the acceleration of the position instruction θ* is, the greater the torque instruction T* is generated at the points A, B, C and D. Generally, an upper limit is provided for the torque instruction T* due to limitations in hardware. The torque T* is limited so that the torque does not increase higher than the upper limit. Where a fluctuation of the second order differential of the electric motor position instruction θM* becomes excessive at the points A, B, C and D, the torque instruction T* is limited. If the torque T* is limited, the controlling apparatus is not able to output an adequate torque waveform to suppress vibrations while holding high-speed response. Thus there was a problem in that it takes considerable time for vibration convergence of the control object position θL.
It is therefore an object of the invention to provide a method for controlling an electric motor, by which vibrations of the electric motor and a control object (load) can be suppressed while maintaining high-speed response of an electric motor and a control object without depending on instruction patterns and characteristics of a control object in a controlling apparatus having low mechanical rigidity of a control object and a coupling portion, etc., between an electric motor and a control object, and to provide an apparatus for controlling the same. In detail, it is an object of the invention to provide a method for controlling an electric motor and apparatus for controlling the same, which prevent the torque instruction from being limited when it becomes excessive, without depending on instruction patterns and characteristics of a control object.
It is another object of the invention to provide a method for controlling an electric motor and apparatus for controlling the same, which automatically and optimally suppress vibrations of the electric motor and control object in response to the quantity of state of a control system (unevenness and chronological changes in the characteristics of individual controlling apparatuses (including control objects) and/or differences in the history up to the quantity of state thereof).